Formal verification is having a moment.

This is something we strongly advocate (and provide as a service).

We've put a 6-part explainer series together explaining vericoding. Here's the first:

What is vericoding.

#vericoding #formalverification

a second millennium prize has hit the stochastic parrot

Every maths-related "proof" released by an AI company should be treated as though posted to arXiv by someone unaffiliated with any math department anywhere and with no existing track record of math research. If the latter would be assumed to be faulty or a quack at worst, why are we assuming better from tech companies' text generating linear algebra systems #math #themathpocalypseisf…

It's not solving the Millennium Prize problem, which is to show that Yang-Mills theory without fermions makes sense and has a "mass gap", meaning that it predicts a glueball of some nonzero mass. But proving Yang-Mills theory makes sense is a big first step. And getting fermions into the theory is also good. Note how they're working with all the key bigshots in this particular su…

Whoa!!!! Showing that two quantum field theories in common use actually make rigorous sense: Yang-Mills theory, and QCD, which is Yang-Mills theory plus fermions (namely quarks). This will be HUGE if true. For many decades, mathematical physics has been stuck on this problem. (1/2)

An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4

Even experts debate what a formal proof actually establishes.

If experts question what a proof guarantees, how can ordinary users judge a project's claims?

Verification should be independently accessible, not something users must simply trust.

My papers have certainly benefited from peer review. It can be a lovely form of anonymous collaboration. But it can also get out of hand to the point where the referee wants to be a coauthor

Learn about the SAIR Foundation and its developing platform, its AI models, mathematical research tools, and how research teams can apply for access.

Learn more: www.openmathmodel.org

SAIR is also seeking collaborators to develop AI models tailored more specifically to mathematics and is working to make the platform available at no cost to researchers at academic institutions.

The platform offers tools to help researchers explore mathematical ideas, discuss and summarize complex arguments, and work on formalizing mathematics using Lean.

The American Mathematical Society (AMS) applauds efforts like SAIR’s to develop a platform that incorporates norms around research standards and broadens access for mathematicians to conduct AI-assisted research.

The Science and AI Research (SAIR) Foundation recently launched its Open Math OS, an emerging platform designed to expand access to open AI models for mathematical work.

Exploring New Possibilities in AI and Mathematics: SAIR Launches Open Math OS

@tristanbuckmaster I often agree with mathematicians on AI, and with a lot of your guest post on Tao's blog. But I traced the "distasteful" quote back through the timeline, and I'm not convinced OpenAI contradicted itself, read in its own terms. I'd be glad to hear if I've missed something. https://blog.kolen.dev/link/buckmaster-distasteful.html #math #AI

The AMS is committed to connecting our community and fostering thoughtful, informed conversations as the impact of AI on mathematics continues to unfold.

Have a resource to recommend? Email: ai@ams.org

Explore resources: www.ams.org/ai/ai

The web page brings together resources on AI-assisted research, proof verification, mathematics education, emerging tools, and expert perspectives with opportunities to explore new ideas, learn from others, and engage with the evolving role of AI in mathematics.

The American Mathematical Society (AMS) has launched AI and Mathematics: Selected Resources, a curated collection to help mathematicians explore the opportunities, questions, and evolving discussions surrounding AI and mathematical discovery.

OpenAI’s AI-generated proofs of Millennium Prize Problems have triggered MIT math students’ fears about displacement and career futures.

Interesting site. Here you get paid for solving #math problems. No academic credentials needed. Just a lean certificate that the proof is correct and you get paid in cryptocurrency. Many will try to use #AI to solve them. https://conjectures.io/

Another way in which AI is undermining the human practice of mathematics

Does anyone else find it offensive that the same rich, influential #math guys who are propping up this #LLM charade have now decided that we need to focus on the importance of teaching and other "soft" aspects of the field now that "AI has solved math"? Like the reason people accepted your use of money to dictate the direction of the field was because they thought (1) you were…

OpenAI, Anthropic and the Simons Institute have promised to contribute enough money to pay a typical US math postdoc to work for 2 months on each of the 719 papers OpenAI recently released: $15,000,000/(719 ×$125,000) ≈ 1/6 where $125,000 is typical annual salary + benefits + overhead.

Overwhelmed by the number of manuscripts, some math journals are temporarily closing submissions

I've been thinking about the AI generated mathematical proofs thing and I actually feel like I'm not as bothered about it as I was initially.

provided of course that in the process of adding an AI generated proof to the corpus of true mathematical statements humans are still checking the work.

How to formalize all of mathematics. ~ Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash, Adam Topaz. https://xenaproject.wordpress.com/2026/10/16/how-to-formalize-all-of-mathematics/ #LeanProver #ITP #AI4Math

There's never been a better time to go into math https://lobste.rs/s/wzgadv #video #math https://www.youtube.com/watch?v=LKrwhjOI8Nc

I also disagree about AI not having any instinct of self-preservation. It's certainly a plausible view, but there are arguments explaining why it would develop such instincts, and there seems to be evidence that they are actually doing so to some extent, and I would expect that to increase.

Can AI help with the most tedious, time-consuming parts of formal verification?

In a recent experiment, Galois's Marios Georgiou explored "proof grinding" with LLMs. The strongest results came when the LLM received one precise property to prove or break at a time.

This is just the beginning of a wider project -- I'm looking forward to seeing where it will go. More generally, I am (like many people) excited by the possibilities that imaginative interfaces will bring to mathematical reasoning.

Many people just starting out on Lean formalization have enjoyed playing the Natural Numbers Game. Now Autumn Mapes has produced Visual Lean, isomorphic to the original but playable in a lovely intuitive way with clicking and dragging rather than typing.

leangame.autumnofautumn.com

Tl;dr (and it is long): I don't have a p(doom), but in particular I can't confidently say that my p(doom) is close to zero, which is a worrying position to be in. I also try to encourage mathematicians to think harder about the question and maybe consider working on AI safety.

Many people with relevant expertise think there's a real chance that AI could kill us all in the not too distant future. Others disagree. I've written a post, aimed principally at mathematicians, detailing my struggles to decide what to make of this.

gowers.wordpress.com/2026/10/16/h...

Dumping 722 synthetic math proofs on GitHub while ignoring academic pleas to stop hoarding proprietary models. Solving the universe with brute force, then offering to sponsor the afterparty.

it is a little funny that all of these openai math proofs aren't even like lean-checked so they have to keep pulling them because of sign errors and other silly simple mistakes. They're automating away the job of "weird guy who sends any mathematician with an university email their bad fermat proof"

This is the whole problem. They are flooding the zone with shit “proofs” that AI works, from math problems to even the meta shit of AI detection in literature (and not surprising it’s mostly black and brown authors that get accused) without any independent verification of their “proof”

"We found that the most gendered experience wasn’t work-life balance, the focus of most retention efforts. It was feeling devalued, in formal evaluations, but particularly in everyday interactions. Unlike every other topic, the gender gap in devaluation was larger among more senior faculty. " Read the study. https://www.science.org/doi/10.1126/sciadv.adi2205 #womeninstem #math #maths

Prof Gio explains how math is in fact about showing your work. The point of math questions is to prompt the mathematics required to find the solution. Millennium Prize Problems are supposed to be an impetus for new theories that will revolutionize the world. LLMs saying 42 is 🤷‍♀️ #Mathematics #Math https://www.youtube.com/watch?v=KqiDqJMxg6o

I’m sorry but this is nonsense. You can soften it a bit to be not nonsense. It solved the Millennium Prize problem in a uninformative or disappointing way. It solved it via a loophole even if you want, although that’s really pushing it. But they did solve the problem as it is explicitly stated.

Great post -- Sophie makes an important point: the results OpenAI announced with great fanfare are "normal for the current state of technology".

The credit goes above all to the data -- the communal knowledge of mathematicians they relied to train their LLM